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Proof step 189 from proof addarray-put-01 (previous step)

0 ≤ i0, 0 ≤ i0 + j, 0 < j, is_indexkey(sk) ⊦ (addarray(r, ty, i0 + j + 1, st)[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk]), sk = j ', j = 0, sk = _type, sk = _length

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 148:
⊦ is_indexkey(sk) ↔ (∃ i. sk = i ')
Proof step 188:
0 ≤ i0, 0 ≤ i0 + j, 0 < j, ∃ i. sk = i ' ⊦ (addarray(r, ty, i0 + j + 1, st)[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(j)) + val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk]), sk = j ', j = 0, sk = _type, sk = _length

Rule argument

[speclemmaarg: ,is_indexkey(sk) ↔ (∃ i. sk = i ') ,[sk] → [sk] ,F ,storekey , ,ex-04 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk)]]